%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:52:38 AM UTC 2026
% Result : Theorem 8.85s 1.53s
% Output : CNFRefutation 8.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 6 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 34 ( 5 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kelley_p90a,axiom,
! [X0,X1,X2] : 'a$ucontinuous$ufunction$ufrom$uonto'('the$uprojection$ufunction'(X0,X1,X2),'the$uproduct$utop$uspace$uover'(X1,X2),apply(X1,X0)) ).
fof(kelley_3_2,axiom,
! [X0,X1,X2,X3] : 'an$uopen$ufunction$ufrom$uonto'('the$uprojection$ufunction'(X0,X1,X2),'the$uproduct$utop$uspace$uover'(X3,X2),apply(X3,X0)) ).
fof(kelley_p_147e,axiom,
! [X0,X1,X2] :
( ( 'a$ulocally$ucompact$utop$uspace'(X1)
& 'a$ucontinuous$ufunction$ufrom$uonto'(X0,X1,X2)
& 'an$uopen$ufunction$ufrom$uonto'(X0,X1,X2) )
=> 'a$ulocally$ucompact$utop$uspace'(X2) ) ).
fof(kelley_5_19a,conjecture,
! [X0,X1] :
( 'a$ulocally$ucompact$utop$uspace'('the$uproduct$utop$uspace$uover'(X0,X1))
=> ! [X2] : 'a$ulocally$ucompact$utop$uspace'(apply(X0,X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'a$ulocally$ucompact$utop$uspace'('the$uproduct$utop$uspace$uover'(X0,X1))
=> ! [X2] : 'a$ulocally$ucompact$utop$uspace'(apply(X0,X2)) ),
inference(negate_conjecture,[status(cth)],[kelley_5_19a]) ).
cnf(c0,plain,
'a$ucontinuous$ufunction$ufrom$uonto'('the$uprojection$ufunction'(X0,X1,X2),'the$uproduct$utop$uspace$uover'(X1,X2),apply(X1,X0)),
inference(clausification,[status(esa)],[kelley_p90a]) ).
cnf(c1,plain,
'an$uopen$ufunction$ufrom$uonto'('the$uprojection$ufunction'(X0,X1,X2),'the$uproduct$utop$uspace$uover'(X3,X2),apply(X3,X0)),
inference(clausification,[status(esa)],[kelley_3_2]) ).
cnf(c2,plain,
( 'a$ulocally$ucompact$utop$uspace'(X2)
| ~ 'a$ulocally$ucompact$utop$uspace'(X1)
| ~ 'a$ucontinuous$ufunction$ufrom$uonto'(X0,X1,X2)
| ~ 'an$uopen$ufunction$ufrom$uonto'(X0,X1,X2) ),
inference(clausification,[status(esa)],[kelley_p_147e]) ).
cnf(c3,plain,
'a$ulocally$ucompact$utop$uspace'('the$uproduct$utop$uspace$uover'(sK10,sK11)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c4,plain,
~ 'a$ulocally$ucompact$utop$uspace'(apply(sK10,sK12)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'a$ulocally$ucompact$utop$uspace'('the$uproduct$utop$uspace$uover'(X3,X2))
| 'a$ulocally$ucompact$utop$uspace'(apply(X3,X0))
| ~ 'a$ucontinuous$ufunction$ufrom$uonto'('the$uprojection$ufunction'(X0,X1,X2),'the$uproduct$utop$uspace$uover'(X3,X2),apply(X3,X0)) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d1,plain,
( 'a$ulocally$ucompact$utop$uspace'(apply(X0,X2))
| ~ 'a$ulocally$ucompact$utop$uspace'('the$uproduct$utop$uspace$uover'(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
'a$ulocally$ucompact$utop$uspace'(apply(sK10,X0)),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP021+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 20:33:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.85/1.53 % SZS status Theorem for theBenchmark.p
% 8.85/1.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------